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A260669
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Number of unordered pairs of partitions of n with no common parts.
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9
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1, 0, 1, 2, 6, 8, 24, 30, 74, 110, 219, 309, 651, 870, 1608, 2394, 4085, 5756, 9931, 13785, 22724, 32300, 50404, 70862, 111540, 153756, 232868, 326259, 484090, 667015, 986082, 1345566, 1951216, 2673588, 3805742, 5179213, 7348514, 9895254, 13845750, 18681896
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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n = 6 has A000041(6) = 11 partitions: [6], [5,1], [4,2], [4,1,1], [3,3], [3,2,1], [3,1,1,1], [2,2,2], [2,2,1,1], [2,1,1,1,1], [1,1,1,1,1,1]; the following table shows the number of common parts of the pairs of these partitions, e.g. row i, col f: number of common parts of [2,2,1,1] and [3,2,1] = 2:
. -------------------+---+---+---+---+---+---+---+---+---+---+---+
. | a | b | c | d | e | f | g | h | i | j | k |
. ---+---------------+---+---+---+---+---+---+---+---+---+---+---+
. a | [6] | 1 |
. b | [5,1] | 0 2 |
. c | [4,2] | 0 0 2 |
. d | [4,1,1] | 0 1 1 3 |
. e | [3,3] | 0 0 0 0 2 |
. f | [3,2,1] | 0 1 1 1 1 3 |
. g | [3,1,1,1] | 0 1 0 2 1 2 4 |
. h | [2,2,2] | 0 0 1 0 0 1 0 3 |
. i | [2,2,1,1] | 0 1 1 2 0 2 2 2 4 |
. j | [2,1,1,1,1] | 0 1 1 2 0 2 3 1 3 5 |
. k | [1,1,1,1,1,1] | 0 1 0 2 0 1 3 0 2 4 6 |
. ---+---------------+---+---+---+---+---+---+---+---+---+---+---+
The table contains 24 zeros, therefore a(6) = 24.
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PROG
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(Haskell)
a260669 = flip div 2 . a054440
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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